Q. 10

Mark the correct alternative in each of the following:

The solution of the differential equation represents a circle when

A. a = b

B. a = –b

C. a = –2b

D. a = 2b

Answer :

By Variable separable,

(by + f) dy = (ax + g) dx

Integrating both sides

∫ (by + f) dy = ∫ (ax + g) dx

by2 + 2fy = ax2 + 2gx + C

Where C’ = 2C

We know general solution of circle is

(x – h)2 + (y – k)2 = r2

Where (h, k) is center of the circle and r is radius.

By completing square method

Now to form above equation as equation of circle we need

i.e. a = -b

= (B)

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